How do you verify the identity #(tanx-secx)/(tanx+secx)=(tan^2x-1)/(sec^2x)#?

1 Answer
Apr 5, 2018

We have:

#(sinx/cosx - 1/cosx)/(sinx/cosx + 1/cosx) = (sin^2x/cos^2x- 1)/(1/cos^2x)#

#((sinx -1)/cosx)/((sinx +1)/cosx) = ((sin^2x - cos^2x)/cos^2x)/(1/cos^2x)#

#(sinx - 1)(sinx+ 1) = sin^2x - cos^2x#

#sin^2x - 2sinx - 1= sin^2x - cos^2x#

#sin^2x - 2sinx - (sin^2x + cos^2x) = sin^2x - cos^2x#

#-2sinx - cos^2x = sin^2x - cos^2x#

Since #-2sinx != sin^2x#, this identity is false.

Hopefully this helps!